## Abstract

We present a theoretical basis for supporting subjective and conditional probabilities in deductive databases. We design a language that allows a user greater expressive power than classical logic programming. In particular, a user can express the fact that A is possible (i.e. A has non-zero probability), B is possible, but (A {n-ary logical and}B) as a whole is impossible. A user can also freely specify probability annotations that may contain variables. The focus of this paper is to study the semantics of programs written in such a language in relation to probability theory. Our model theory which is founded on the classical one captures the uncertainty described in a probabilistic program at the level of Herbrand interpretations. Furthermore, we develop a fixpoint theory and a proof procedure for such programs and present soundness and completeness results. Finally we characterize the relationships between probability theory and the fixpoint, model, and proof theory of our programs.

Original language | English (US) |
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Pages (from-to) | 191-235 |

Number of pages | 45 |

Journal | Journal of Automated Reasoning |

Volume | 10 |

Issue number | 2 |

DOIs | |

State | Published - Jun 1993 |

Externally published | Yes |

## Keywords

- Subjective and conditional probabilities
- deductive databases
- probability theory

## ASJC Scopus subject areas

- Software
- Computational Theory and Mathematics
- Artificial Intelligence